Goodarzi, K. (2018). Order reduction and μ-conservation law for the non-isospectral KdV type equation a with variable-coefficients. Theory of Approximation and Applications, 12(1), 29-41.

Khodayar Goodarzi. "Order reduction and μ-conservation law for the non-isospectral KdV type equation a with variable-coefficients". Theory of Approximation and Applications, 12, 1, 2018, 29-41.

Goodarzi, K. (2018). 'Order reduction and μ-conservation law for the non-isospectral KdV type equation a with variable-coefficients', Theory of Approximation and Applications, 12(1), pp. 29-41.

Goodarzi, K. Order reduction and μ-conservation law for the non-isospectral KdV type equation a with variable-coefficients. Theory of Approximation and Applications, 2018; 12(1): 29-41.

Order reduction and μ-conservation law for the non-isospectral KdV type equation a with variable-coefficients

^{}Department of Mathematics, Broujerd Branch, Islamic Azad University, Broujerd, Iran.

Abstract

The goal of this paper is to calculate of order reduction of the KdV type equation and the non-isospectral KdV type equation using the μ-symmetry method. Moreover we obtain μ-conservation law of the non-isospectral KdV type equation using the variational problem method.

Order reduction and μ-conservation law for the non-isospectral KdV type equation a with variable-coefficients

References

[1]H. Airault, Rational solutions of Painleve equation, Studies in Applied Mathematics , 1979, 61, P.31{53. [2]T.B. Benjamin, J.L. Bona and J.J. Mahony, Model equations for long waves in nonlinear dispersive systems, Trans. R. Soc. (Lond) ser.A, 1992, 272, P.234-356. [3]W. Bluman, F. Cheviakov, C. Anco, Construction of conservation law: how the direct method generalizes Nother's theorem, Group analysis of dierential equations and integrability, 2009, 12 P.1{23. 40 x [4]J.L. Bona, Bryant, P.J., A mathematical model for long waves gener- ated by wave makers in nonlinear dispersive systems, Proc. Cambridge Phil. Soc., 1973, 4, P.12{34. [5]G. Cicogna, G. Gaeta, P. Morando, On the relation between standard and -symmetries for PDEs, J. Phys. A. , 2004, 37, P. 9467{9486. [6]G. Cicogna, G. Gaeta, Norther theorem for -symmetries, J. Phys. A., 2007, 40, P.11899{11921. [7]G. Gaeta, P. Morando, On the geometry of lambda-symmetries and PDEs reduction, J. Phys. A., 2004, 37, P.6955{6975. [8]G. Gaeta, Lambda and mu-symmetries, SPT2004 , World Scientic, Singapore, 2005. [9]KH. Goodarzi, M.Nadjakhah, -symmetry and -conservation law for the extended mKdV equation, JNMP (2014),3, P.371{381. [10]D.J.Korteweg, G. de Vries, On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves, Phil. Mag. 1895, 39, P.422{443. [11]A. Kudryashov, I. Sinelshchikov, A note on the Lie symmetry analysis and exact solutions for the extended mKdV equation, Acta. Appl.Math., 2011, 113, 41{44. [12]C. Muriel, J.L. Romero, New methods of reduction for ordinary dierential equation, IMA J. Appl. Math., 2001, 66, P.111{125. [13]C. Muriel, J.L. Romero, C 1 -symmetries and reduction of equation without Lie point symmetries, J. Lie Theory, 2003, 13, P.167{188. [14]C. Muriel, J.L. Romero, P.J. Olver, Variationl C 1 -symmetries and EulerLagrange equations, J. Di. Eqs, 2006, 222, P.164{184. [15]C. Muriel, J.L. Romero, Prolongations of vector elds and the invariantsby-derrivation property, Theor. Math. Phys., 2002, 133,P.1565{1575. [16]P.J. Olver, Applications of Lie Groups to Dierential Equations, New York, 1986. [17]C. Vasconcellos, P. N. da Silva, Stabilization of the linear Kawahara equation, Applied and Computational Mathematics, 2015, 3, P. 45-67. 41